[1] Zhang Changyou, Zhu Changming, Lin Zhongqin,. Suppression strategy for parametrically excitedlateral vibration of mass-loaded string [J]. Journal of Southeast University (English Edition), 2004, 20 (2): 165-169. [doi:10.3969/j.issn.1003-7985.2004.02.008]

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Suppression strategy for parametrically excitedlateral vibration of mass-loaded string()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

20

Issue:

2004 2

Page:

165-169

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2004-06-30

Info

Title:

Suppression strategy for parametrically excitedlateral vibration of mass-loaded string

Author(s):

Zhang Changyou;  Zhu Changming;  Lin Zhongqin

College of Mechanical and Power Engineering, Shanghai Jiaotong University, Shanghai 200030, China

Keywords:

mass-loaded string;  parametric resonance;  vibration absorber

PACS:

O322;TM726.4

DOI:

10.3969/j.issn.1003-7985.2004.02.008

Abstract:

This paper discusses a simple way to suppress the parametrically excited lateral vibration of a mass-loaded string. Supposing that the mass at the lower end of the string is subjected to a vertical harmonic excitation and neglecting the higher order vibration modes, the equation of motion for the mass-loaded string can be represented by a Mathieu’s equation with cubic nonlinearity. According to the theory of the Mathieu’s equation, in the mass-loaded string system, when the vertical vibration frequency of the mass approaches twice the natural frequency of the string lateral vibration, once the vertical vibration amplitude of the mass exceeds a critical value, the parametric resonance will occur in the string. To avoid the parametric resonance, a vibration absorber, composed of a thin beam and two mass blocks attached at both sides of the beam symmetrically, is proposed to install with the mass to reduce its vertical vibration, and ultimately suppress the lateral vibration of the string. Such a suppression strategy is finally validated by experiments.

References:

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[10] Terumichi Y, Ohtsuka M, Yoshizawa M, et al. Nonstationary vibrations of a string with time-varying length and a mass-spring system attached at the lower end [J]. Nonlinear Dynamics, 1997, 12(1): 39-35.
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Memo

Memo:

Biographies: Zhang Changyou(1975—), male, graduate; Zhu Changming(corresponding author), male, professor, zhuchangming@sjtu.edu.cn.

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